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Solution1

# Solution1 - Answers to HW 1 1 Sample space is composed of...

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Answers to HW 1 1. Sample space is composed of 52 elements such as {A,2,3,4,5,6,7,8,9,10,J,Q,K} associated with 4 different suits. For instance, the probability of event {A,J} is assigned as p(A,J) = 8/52=2/13 2. 1/3; 2/3; b-a, if b a . 3. p(L|U)=0, P(C|U)= 1 7 12 1 2 31 12 7 = + 4. P(U|C)= 1 1 12 1 1 3 12 6 = + , P(M|C)= 1 2 6 1 1 3 12 6 = + 5. The expected payoff of player 2 is 1 1 1 2 2 1 1 2 2 0 ( 2) ( 2 2) 1 3 3 5 5 5 3 5 5 5 + + + + + + = . 6. Each 1,2,4,5 remaining in the urn is equally likely to be drawn with a 1/4 chance. 7. Proportion Duck = 3 3 13 1 2 3 4 3 5 20 .65 + = = P(Round|Lamb)= 2 2 3 5 16 21 2 2 1 1 3 5 3 4 .76 = = + P(Bone|Duck)= 3 1 3 4 5 13 3 3 1 2 3 4 3 5 .38 = = + 8. (i) just one positive test result. ( ) ( | ) ( ) 0.95 0.05 ( | ) 0.250 ( ) ( | ) ( ) ( |~ ) (~ ) 0.95 0.05 0.15 0.95 p cont p cont p cont p cont p p cont p cont
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